Self-Stabilization, Byzantine Containment, and Maximizable Metrics: Necessary Conditions

TL;DR

This paper investigates the fundamental limitations of constructing maximum metric trees in distributed systems that are both self-stabilizing and Byzantine fault-tolerant, providing necessary conditions for such constructions.

Contribution

It establishes two necessary conditions that must be met to build maximum metric trees under combined self-stabilization and Byzantine fault conditions.

Findings

Identifies fundamental impossibility results for certain system configurations.

Provides necessary conditions for the existence of resilient maximum metric trees.

Abstract

Self-stabilization is a versatile approach to fault-tolerance since it permits a distributed system to recover from any transient fault that arbitrarily corrupts the contents of all memories in the system. Byzantine tolerance is an attractive feature of distributed systems that permits to cope with arbitrary malicious behaviors. We consider the well known problem of constructing a maximum metric tree in this context. Combining these two properties leads to some impossibility results. In this paper, we provide two necessary conditions to construct maximum metric tree in presence of transients and (permanent) Byzantine faults.